Officials at government-backed mortgage giant Fannie Mae concluded years ago that the company could “reduce its losses substantially” by lowering loan amounts for some troubled borrowers, according to internal documents cited Tuesday by the top Democrat on the House oversight committee.

The new insights into Fannie Mae’s analyses about the potential benefits of so-called principal reduction surfaced in a letter from Rep. Elijah E. Cummings (D-Md.) to Edward J. DeMarco, the acting director of the independent agency that oversees Fannie Mae and Freddie Mac.

Since being appointed head of the Federal Housing Finance Agency (FHFA) in 2009, DeMarco has refused to allow Fannie and Freddie to write down loan balances, in part because he worries that some homeowners would stop paying their mortgages to get relief, ultimately costing taxpayers more money. He has been steadfast in his disapproval in recent months despite growing pressure from Obama administration officials and House Democrats to allow principal reductions.

In the letter, Cummings and another committee member, Rep. John F. Tierney (D-Mass.), cite documents provided by a former Fannie employee. They accuse DeMarco of withholding key documents from the oversight committee and of failing to mention Fannie’s findings during past testimony, in which DeMarco explained his reasons for opposing reductions in loan balances.

“We have very serious concerns about your public statements, your previous responses to us, and your failure to provide Congress with complete and accurate information about these important matters,” the two men wrote.

The letter details a specific pilot program that Fannie Mae officials considered creating in conjunction with Citibank beginning in 2009. Under the program, the loan balances of qualified homeowners would have been reduced to help them remain in their homes, with the homeowners agreeing to share any profits on the future sale of the home.

The letter cites presentations in which Fannie officials estimated that the program would cost $1.7 million, while the benefits could have saved more than $410 million. Despite its approval by a company risk officer in April 2010, the program was killed that July, and the documents provide no clear explanation why, Cummings said.

“This was not merely a missed opportunity, but a conscious choice that appears to have been based on ideology rather than Fannie Mae’s own data and analyses,” the letter asserted.

Cummings noted that in November 2010, after the pilot program had been suspended, some Fannie officials continued to make the case for principal reductions. He cited one 30-page research paper that concluded the firm “might reduce its losses substantially in many cases by writing down principal.”

The letter marks the latest in a long struggle by Cummings, other lawmakers and administration officials to persuade DeMarco to allow Fannie and Freddie to write down loans to help homeowners who owe far more than their homes are worth.

Later Tuesday, DeMarco responded to the two Democratic lawmakers with a letter of his own, expressing dismay over their suggestion that his motives were based on ideology and that the FHFA’s responses had been “anything but in keeping with the professionalism expected of this agency.” He also accused Cummings and Tierney of releasing “selective elements of the proprietary and confidential materials you received.”

DeMarco noted that the FHFA had explored multiple pilot programs in recent years and that documents the agency previously had provided to the oversight committee “reflect an open and robust interest in this topic, enthusiasm for meeting the goals of finding a workable approach for a pilot program and adherence to review of ideas from all sides, including gathering data and undertaking its analysis.”

DeMarco also attached a letter that the FHFA’s general counsel had sent to Cummings and Tierney in April that included a detailed summary of several pilot programs that Fannie Mae and Freddie Mac had considered in recent years, including the one with Citibank that was terminated.

DeMarco has long said that more study is needed and that he prefers other tools to help aid struggling homeowners, including helping refinance borrowers into loans with lower interest rates or reducing payments and extending the length of the loan.

Fannie and Freddie “have been reviewing principal forgiveness alternatives. Both have advised me that they do not believe it is in the best interest of the companies to do so,” DeMarco told lawmakers during a Senate hearing in February, adding, “I believe that assuring that we’re taking appropriate steps to provide assistance to troubled borrowers is very much at the heart of what we’re trying to do, but we need to do so in a way in which we are meeting our mandate to protect the taxpayers.”

During a speech in April at the Brookings Institution, DeMarco cited preliminary new data showing that Fannie and Freddie could save an estimated $1.7 billion by taking advantage of greater incentives from the Treasury Department to write down the principal for some homeowners.

But he said those calculations alone were not enough to persuade him to allow Fannie and Freddie to offer principal writedowns. “A key risk in principal forgiveness targeted at delinquent borrowers is the incentive created for some portion of the current borrower population to cease paying in search of a principal forgiveness modification,” DeMarco said in his speech.

That same day, DeMarco said he expected the FHFA to wrap up a detailed analysis about the merits of principal reductions by the end of April. On Friday, however, the agency said it would need more time to make a final decision.

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